Acta Psychologica Sinica

Abstract

In the past years, c parameter was viewed as guessing parameter, and what it means remains unclear for the IRT researchers. The four-parameter logistic model was given little attention, and not applied in the practice. In this thesis the authors examined the meaning of c and γ parameters in logistic model by proposing that c and γ parameters would improve the ability of estimation when the subjects make responses on items of different b value.

After designing an ideal test and responses from subjects that can give either right or wrong responses to one extra item with varying degrees of difficulty, we compile a program for estimating the abilities of subjects with method of Maximum Likelihood Estimation (MLE). It analyzes the influences of c parameter and γ parameter on agreement of the abilities and various responses drawn from the subjects.

(1) When estimating the abilities of the subjects within one-parameter or two-parameter logistic model, two kinds of disagreement existed. (2) Estimating the abilities of the subjects after introducing c parameter on the basis of a two-parameter model, the first disagreement could be rectified. However, the second disagreement remained and a third disagreement appeared. (3) Estimating the abilities of the subjects again after introducing γ parameter, it was discovered that the second disagreement was rectified, but the first disagreement still existed and a fourth disagreement appeared. (4) Forming four-parameter Logistic model by introducing c parameter and γ parameter simultaneously and estimating the abilities one more time, the model rectified all four disagreements.

In future research, the present findings need to be replicated in other conditions: (1) when the subjects make responses to two or more items of different b value; (2) on the assumption that the subject’s ability distribution has been known, estimating the abilities of the subjects with the other two methods: Maximum A Posterior Estimation (MAPE) and Expected A Posterior Estimation (EAPE).

To summarize, C parameter is the probability of guessing that all the subjects make right response to the item that item difficulty is larger than the ability of subjects, and adding c parameter can improve the ability estimation in such case. γ parameter is the probability of mistakes that all subjects make wrong response to the item which difficulty is less than the ability of subjects, and adding γ parameter can improve the ability estimation in that case. And so, the four-parameter logistic model is advocated.

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